It is normal that the message that show up in your Buyer-seller message center will not have any links or hyperlinks as the links are removed by Amazon. The email received by the Buyer will show up with the hyperlinks.
In addition, the one test email from the Action option will not have a working hyperlink. The one-time send test email was not generated using an actual order ID, so there is no data to use for the one-time test email. You can make the campaign status under Test to receive the test email generated with actual order ID. Hence, the links and image will work.